I am in the first year of my PhD research (in Europe) in Biostatistics and I have a day-to-day supervisor, however he is not a full professor so he cannot be my promotor. Our department head is, but I would technically obtain the PhD at a department of Medicine/Epidemiology instead of (bio)statistics. Would this have a big effect on my future prospects if I wanted to continue in (bio)statistics, or are the topic and connections you build more important? We are considering looking for someone more statistical/mathematical as a promotor or copromotor, would this change much (on top of the influence they would have on the content of the thesis)?
So in short, if the content of the thesis/project is the same, does the name or work area of the promotor have a lot of influence on future prospects?